Geodesic
Solution of $n$-phase $\mathbb R$-linear conjugation problem
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2011), pp. 81-88

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We consider the problem of the distribution of power fields of various physical nature in a piecewise homogeneous planar medium consisting of several homogeneous components separated by branches of confocal hyperbolas. We reduce this problem to the linear conjugation problem and solve the latter analytically.
Keywords: heterogeneous media, $\mathbb R$-linear conjugation problem, analytic functions. 
@article{IVM_2011_4_a7,
     author = {T. V. Nikonenkova},
     title = {Solution of $n$-phase $\mathbb R$-linear conjugation problem},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {81--88},
     publisher = {mathdoc},
     number = {4},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2011_4_a7/}
}
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T. V. Nikonenkova. Solution of $n$-phase $\mathbb R$-linear conjugation problem. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2011), pp. 81-88. http://geodesic.mathdoc.fr/item/IVM_2011_4_a7/